Monday, October 08, 2012

John Wheeler said that the "basis of all mathematics
is 0 = 0". All mathematical structures can be derived from something
called "the empty set", the set that contains no elements. Say this set
corresponds to zero; you can then define the number 1 as the set that
contains only the empty set, 2 as the set containing the sets
corresponding to 0 and 1, and so on. Keep nesting the nothingness like
invisible Russian dolls and eventually all of mathematics appears...

...Reality may come down to mathematics, but mathematics comes down to nothing at all.

That may be the ultimate clue to
existence - after all, a universe made of nothing doesn't require an
explanation. Indeed, mathematical structures don't seem to require a
physical origin at all. "A dodecahedron was never created," says Max Tegmark.

"To be created, something
first has to not exist in space or time and then exist." A dodecahedron
doesn't exist in space or time at all, he says - it exists
independently of them. "Space and time themselves are contained within
larger mathematical structures," he adds. These structures just exist;
they can't be created or destroyed.

That raises a big question: why is the
universe only made of some of the available mathematics? "There's a lot
of math out there," says Brian Greene. "Today only a tiny sliver of it has a
realisation in the physical world...

..."I believe that physical existence and mathematical
existence are the same, so any structure that exists mathematically is
also real," says Tegmark.

So what about the mathematics our
universe doesn't use? "Other mathematical structures correspond to other
universes," Tegmark says. He calls this the "level 4 multiverse", and
it is far stranger than the multiverses that cosmologists often discuss.
Their common-or-garden multiverses are governed by the same basic
mathematical rules as our universe, but Tegmark's level 4 multiverse
operates with completely different mathematics.